Electrical Impedance Tomography by Elastic Deformation

Abstract

Abstract. This paper presents a new algorithm for conductivity imaging. Our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations. Using asymptotics of the elds in the presence of small volume inclusions, we relate the pointwise values of the energy density to the measured data, through a nonlinear PDE. Our algorithm is based on this PDE and takes full advantage of the enriched data. We give numerical examples that illustrate the performance and the accuracy of our approach.

Artificial conditions for the linear elasticity equations

“…This problem enters the general framework of local perturbations for elliptic problems, which have been deeply studied. Among others, let us mention the following works using potential theory [38,5,3,4] and the reference monographs [30,31] for multiscale expansions. Following [10,36], the solution of (1.1) is given to first order by…”

Microwave Imaging by Elastic Deformation

“…The aim of this paper is to develop new mathematical tools and inversion methods to address emerging modalities which are of great current interest in the biomedical imaging community and pose challenging mathematical and numerical problems. We want to extend the hybrid approach for conductivity imaging developed in [3] to the microwave regime.…”

“…By non intrusive methods, controlled perturbations inside a domain of interest, e.g., a human body, can be created. As first shown in [3], this allows one to reconstruct the unperturbed medium very accurately by using a standard medical imaging technique, which in the absence of these controlled perturbations, provides very poor resolution.…”

“…This drawback has limited its use so far to anomaly detection [10,11,26]. In the recent work by Ammari et al [3], it was shown that combining these measurements with simultaneous localized ultrasonic perturbations allows to recover the conductivity with good resolution. In fact, we change the EIT problem by the problem of reconstructing the conductivity distribution from the internal electrical energy.…”

“…See, for instance, [1,15]. As highlighted in [3], the resolution is of order the size of the focal spot of the ultrasound perturbation.…”